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Factorization Of Algebraic Expressions — MATHS STD 9 — Question

Rajasthan BoardEnglish MediumSTD 9MATHSFactorization Of Algebraic Expressions2 Marks
Question
Factorize the following expressions: $27x^3 - y^3 - z^3 - 9xyz$
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Answer

We know that
$x^3 + y^3 + z^3 - 3xyz$
$= ( x + y + z)(x^2 + y^2 + z^2 - xy - yz -zx)$
$\therefore 27x^3 - y^3 - z^3 - 9xyz$
$= (3x)^3 + (-y)^3 + (-z)^3 - 3(3x)(-y)(-z)$
$= [3x +(-y) + (-z)][(3x)^2 + (-y)^2 + (-z)^2 - (3x)(-y)(-z)-(-z)(3x)]$
$= (3x - y - z)(9x^2 + y^2 + z^2 + 3xy - yz + 3zx)$

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